Year 2 Use Arrays Reasoning and Problem Solving

[Pages:5]Reasoning and Problem Solving Step 6: Use Arrays

National Curriculum Objectives:

Mathematics Year 2: (2C6) Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers Mathematics Year 2: (2C7) Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (?), division (?) and equals (=) signs Mathematics Year 2: (2C8) Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts Mathematics Year 2: (2C9b) Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

Differentiation:

Questions 1, 4 and 7 (Problem Solving) Developing Draw arrays to match the given amount. Arrays used to solve multiplication, all arrays presented within a grid format. Expected Draw arrays to match the given amount. Arrays used to solve multiplications. Greater Depth Draw arrays to match the given amount. Arrays used to solve multiplications and make deductions from outside known multiplication facts.

Questions 2, 5 and 8 (Reasoning) Developing Identify the odd one out. Arrays used to solve multiplication, all arrays presented within a grid format. Expected Identify the odd one out. Arrays used to solve multiplications. Greater Depth Identify the fact that is not related to the array. Arrays used to solve multiplications and make deductions from outside known multiplication facts.

Questions 3, 6 and 9 (Reasoning) Developing Explain if a given statement is correct. Arrays used to solve multiplication, all arrays presented within a grid format. Expected Explain if a given statement is correct. Arrays used to solve multiplications. Greater Depth Explain if a given statement is correct. Arrays used to solve multiplications and make deductions from outside known multiplication facts.

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Reasoning and Problem Solving ? Use Arrays ? Teaching Information

Use Arrays

1a. Luke has 24 counters and has used them to make the arrays below.

Draw 2 more arrays to match Luke's counters.

Use Arrays

1b. Holly has 18 counters and has used them to make the arrays below.

Draw 2 more arrays to match Holly's counters.

D

PS

D

PS

2a. Use the array to find the odd one out. 2b. Use the array to find the odd one out.

A. 8 x 2 B. 2 lots of 8 C. 2 x 9 Explain your answer.

A. 4 lots of 4 B. 4 x 5 Explain your answer.

C. 4 x 4

D

3a. Rose is making an array.

She says,

R

D

R

3b. Alex is making an array.

He says,

My array shows 5 lots of 2 and 2 lots of 5.

My array shows 3 lots of 6 and 6 lots of 3.

Is she correct? Explain your answer.

Is he correct? Explain your answer.

D

R

D

R

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Reasoning and Problem Solving ? Use Arrays ? Year 2 Developing

Use Arrays

Use Arrays

4a. Charlie has 20 counters and has used 4b. Maisie has 12 counters and has used

them to make the arrays below.

them to make the arrays below.

Draw 2 more arrays to match Charlie's counters.

Draw 2 more arrays to match Maisie's counters.

E

PS

E

PS

5a. Use the array to find the odd one out. 5b. Use the array to find the odd one out.

A. 2 x 3 B. 3 x 2 Explain your answer.

C. 2 lots of 5

A. 4 lots of 5 B. 3 x 5 Explain your answer.

C. 5 x 3

E

R

E

R

6a. Sam is making an array.

6b. Milo is making an array.

He says,

He says,

My array shows 6 lots of 3 and 3 lots of 6.

My array shows 4 lots of 5 and 5 lots of 4.

Is he correct? Explain your answer.

Is he correct? Explain your answer.

E

R

E

R

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Reasoning and Problem Solving ? Use Arrays ? Year 2 Expected

Use Arrays

7a. Jada had 9 counters and has used them to make the array below.

Use Arrays

7b. Harry had 16 counters and has used them to make the array below.

Now Jada has 18 counters.

Draw 3 arrays she could make with 18 counters.

Now Harry has 32 counters.

Draw 3 arrays he could make with 32 counters.

GD

PS GD

PS

8a. Which fact is not related to the array below?

8b. Which fact is not related to the array below?

A. 3 x 6 B. 5 lots of 6 C. 6 x 6 Explain your answer.

A. 8 x 4 B. 2 lots of 8 C. 7 x 5 Explain your answer.

GD

9a. Oscar is making an array.

R GD

R

9b. Jessica is making an array.

He says,

She says,

I can use my array to solve 6 x 5.

I can use my array to solve 4 x 7.

Is he correct? Explain your answer.

Is she correct? Explain your answer.

GD

R GD

R

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Reasoning and Problem Solving ? Use Arrays ? Year 2 Greater Depth

Reasoning and Problem Solving Use Arrays

Developing 1a. Various arrays can be drawn, for example: 2 x 12, 3 x 8. 2a. C because the array does not show 2 x 9. 3a. Rose is incorrect because her array shows 3 lots of 5 or 5 lots of 3.

Expected 4a. 2 arrays to be drawn showing 2 x 10 and 10 x 2. 5a. C because the array does not show 2 lots of 5. 6a. Sam is incorrect because his array shows 3 lots of 7 and 7 lots of 3.

Greater Depth 7a. Various arrays can be drawn, for example: 2 x 9, 6 x 3, 3 x 6 8a. B because there are 3 x 6 which can be used to solve 6 x 6. 9a. Oscar is correct because the array shows 3 x 5 which can be doubled to make 6 x 5.

Reasoning and Problem Solving Use Arrays

Developing 1b. 2 arrays to be drawn showing 2 x 9 and 9 x 2. 2b. B because the array does not show 4 x 5. 3b. Alex is incorrect because his array shows 2 lots of 6 or 6 lots of 2.

Expected 4b. 2 arrays to be drawn showing 3 x 4 and 4 x 3. 5b. A because the arrays does not show 4 lots of 5. 6b. Milo is incorrect because he has 4 lots of 6 or 6 lots of 4.

Greater Depth 7b. Various arrays can be drawn, for example: 8 x 4, 4 x 8, 2 x 16 8b. C because there 2 lots of 8 which can be used to solve 8 x 4. 9b. Jessica is correct because the array shows 2 x 7 which can be doubled to make 4 x 7.

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Reasoning and Problem Solving ? Use Arrays ANSWERS

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